In this paper, we prove that for a set of ten univariate stochastic orders including the usual order, a univariate stochastic order preserves either both, one or none of additivity and multiplication properties over the vector space of real-valued ra...
In this article, we study stochastic orders over an interval. Mainly, we focus on orders related to the Laplace transform. The results are then applied to obtain a bound for heavy-tailed distributions and are illustrated by some examples. We also ind...
Relevant integral stochastic orders share a common mathematical model, they are defined by generators which are made up of increasing functions on appropriate directions. Motivated by the aim to provide a unified study of those orders, we introduce a...
In this article we give theoretical results for different stochastic orders of a log-scale-location family which uses Tsallis statistics functions. These results describe the inequalities of moments or Gini index according to parameters. We also comp...
The One-X property, introduced by Zetocha in a 2023 paper, provides a novel stochastic order with direct implications for constructing arbitrage-free implied volatility surfaces. The current work revisits its theoretical foundations and explores its...
In this paper we focus on providing sufficient conditions for some well-known stochastic orders in reliability but dealing with the discrete versions of them, filling a gap in the literature. In particular, we find conditions based on the unimodality...
In this overview paper, we introduce an application of stochastic orders in wireless communications. In particular, we show how to use stochastic orders to investigate the ergodic capacity results for fast fading Gaussian memoryless multiuser channel...
The fractional stochastic differential equations had many applications in interpreting many events and phenomena of life, and the nonlocal conditions describe numerous problems in physics and finance. Here, we are concerned with the combination betwe...
In this paper, we present order invariance theoretical results for weighted quasi-arithmetic means of a monotonic series of numbers. The quasi-arithmetic mean, or Kolmogorov–Nagumo mean, generalizes the classical mean and appears in many disciplines,...
In this paper, we consider a failed cold standby system and obtain stochastic bounds on the idle time of such systems. We state and prove that if the last spare in the system is exponentially distributed and if the components have log-concave lifetim...
Generalized order statistics (GOSs) are often adopted as a tool for providing a unified approach to several stochastic models dealing with ordered random variables. In this contribution, we first recall various useful results based on the notion of t...
In this article we give sufficient conditions for stochastic order of multivariate uniform distributions on closed convex sets.
The study of spatial and temporal changes in precipitation patterns is important to agriculture and natural ecosystems. These changes can be described by some climate change indices. Because these indices often have skewed probability distributions,...
Expected utility theory is critical for modeling rational decision making under uncertainty, guiding economic agents as they seek to optimize outcomes. Traditional methods often require restrictive assumptions about underlying stochastic processes, l...
This paper is aimed at efficient numerical implementation of the fractional-order generalization of the stochastic Stokes–Darcy model, which has important scientific, applied, and economic significance in hydrology, the oil industry, and biomed...
This paper provides a mathematical proof and theoretical analysis of the one-to-one consistency between higher-order Omega and Almost Stochastic Dominance rules when evaluating fund performance. The consistency between higher-order Omega and Almost N...
In this paper, we introduce the evolve-then-filter (EF) regularization method for reduced order modeling of convection-dominated stochastic systems. The standard Galerkin projection reduced order model (G-ROM) yield numerical oscillations in a convec...
In this paper, we consider two finite mixture models (FMMs) with inverted-Kumaraswamy distributed components’ lifetimes. Several stochastic ordering results between the FMMs are obtained. Mainly, we focus on three different cases in terms of th...
In this article, we introduce and study a new stochastic order of multivariate distributions, namely, the conditional likelihood ratio order. The proposed order and other stochastic orders are analyzed in the case of a bivariate exponential distribut...
Fractional stochastic differential equations are still in their infancy. Based on some existing results, the main difficulties here are how to deal with those equations if the fractional order is varying with time and how to confirm the existence of...
A stochastic dominance (SD) relation can be defined by two different perspectives: One from the view of distributions, and the other one from the view of expected utilities. In the early days, Fishburn investigated SD from the view of distributions,...
Multi-objective optimization (MOO) has become an important method in machine learning, which involves solving multiple competing objective problems simultaneously. Nowadays, many MOO algorithms assume that gradient information is easily available and...
To study the nonlinear dynamic behavior and system stability of a rubbing overhung rotor with viscoelastic and memory-effect damping and random uncertain parameters, this paper introduces a fractional-order modeling and stochastic dynamic analysis me...
The intent of the current study is to explore convex stochastic processes within a broader context. We introduce the concept of unified stochastic processes to analyze both convex and non-convex stochastic processes simultaneously. We employ weighted...
Sample range and the associated functions such as survival function and mean residual life function have found many important applications in the reliability field. In this work, we establish some results that are in two different directions. In the...
This study investigates the computation of fractional and higher integer-order moments for a stochastic process governed by a one-dimensional, non-homogeneous linear stochastic differential equation (SDE) driven by fractional Brownian motion (fBm). U...
This paper studies the finite-time synchronization problem of fractional-order stochastic memristive bidirectional associative memory neural networks (MBAMNNs) with discontinuous jumps. A novel criterion for finite-time synchronization is obtained by...
A numerical technique was developed for solving nonlocal nonlinear stochastic delayed differential equations driven by fractional variable-order Brownian noise. Error analysis of the proposed technique was performed and discussed. The method was appl...
To effectively represent photovoltaic (PV) modules while considering their dependency on changing environmental conditions, three novel mathematical and empirical formulations are proposed in this study to model PV curves with minimum effort and shor...
The portfolio optimization problem is the central problem of modern economics and decision theory; there is the Mean-Variance Model and Stochastic Dominance Model for solving this problem. In this paper, based on the second order stochastic dominance...
This paper focuses on exploring the existence and uniqueness of solutions for a specific type of impulsive fractional-order complex-valued stochastic neural network within the complex domain, a topic hitherto undocumented. The combination of fraction...
In the field of investment, how to construct a suitable portfolio based on historical data is still an important issue. The second-order stochastic dominant constraint is a branch of the stochastic dominant constraint theory. However, only considerin...
This paper is concerned with the problems of mean-square global dissipativity and global asymptotic stability for a class of stochastic fractional-order memristive BAM neural networks with leakage terms and mixed time-varying delays, including discre...
The paper compares portfolio optimization with the Second-Order Stochastic Dominance (SSD) constraints with mean-variance and minimum variance portfolio optimization. As a distribution-free decision rule, stochastic dominance takes into account the e...
Aiming at the problems of poor decomposition quality and the extraction effect of a weak signal with strong noise by empirical mode decomposition (EMD), a novel fault diagnosis method based on cascaded adaptive second-order tristable stochastic reson...
This paper presents a design and evaluation of a fractional-order self optimizing control (FOSOC) architecture for process control. It is based on a real-time derivative-free optimization layer that adjusts the parameters of a discrete-time fractiona...
In this paper, we are concerned with the combinations of the stochastic Itô-differential and the arbitrary (fractional) orders derivatives in a neutral differential equation with a stochastic, nonlinear, nonlocal integral condition. The existence of...
This paper studies the finite-time stability of linear stochastic fractional-order systems with time delay, in which the dynamics are generated by the proportional Caputo fractional derivative of order
Vibration signals are used to diagnosis faults of the rolling bearing which is symmetric structure. Stochastic resonance (SR) has been widely applied in weak signal feature extraction in recent years. It can utilize noise and enhance weak signals. Ho...
In this paper, the fixed-time control for high-order nonlinear multi-agent systems under unknown stochastic time delay is investigated via an event-triggered approach. First of all, RBF neural networks are utilized to approximate the system’s u...
This paper researches the issue of the finite-time combination-combination (C-C) synchronization (FTCCS) of fractional order (FO) chaotic systems under multiple stochastic disturbances (SD) utilizing the nonsingular terminal sliding mode control (NTS...
We investigate pairwise stochastic comparisons of stationary solutions to the linear recurrence
In this article, a new design method for an adaptive fast finite-time controller (FTC) is proposed for the finite-time stability (FTS) issue of a class of high-order stochastic nonlinear systems (HOSNSs) with unknown parameters. Using a power integra...
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In this paper, we compare the performance between systems of ordinary and (Caputo) fractional differential equations depicting the susceptible-exposed-infectious-recovered (SEIR) models of diseases. In order to understand the origins of both approach...
In supply chain management practices, supplier selection (SS) is a critical strategic planning activity that usually constitutes an ex ante decision made under uncertainty, whereas order allocation (OA) represents a subsequent operational decision de...
This paper deals with the issue of the multi-switching sliding mode combination synchronization (MSSMCS) of fractional order (FO) chaotic systems with different structures and unknown parameters under double stochastic disturbances (SD) utilizing the...
We introduce a novel portfolio optimization framework—Distributionally Robust Multivariate Stochastic Cone Order (DR-MSCO)—which integrates partial orders on random vectors with Wasserstein-metric ambiguity sets and adaptive cone structur...
Integrated blisk–shaft rotors represent a critical advancement in aero-engine design, offering enhanced structural integrity and weight reduction. However, their complex dynamic behavior under inherent material uncertainties poses significant c...
This paper investigates a class of distributed fractional-order stochastic differential equations driven by fractional Brownian motion with a Hurst parameter
This study presents a novel approach that integrates model order reduction (MOR) and generalized stochastic collocation (gSC) to enhance robust design optimization (RDO) of viscoelastic damped composite structures under material and geometric uncerta...
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